How do you do this Algebra Problem? Help please.?

Question

1-3i/2-2i What is the quotient written in standard form?

Answer 1

1 - 3i / 2 - 2i

Multiply each side by 2- 2i conjugate numerator and denominator

= (1 - 3i)(2+ 2i) / (2 - 2i)(2 + 2i)

= 2 - 6i + 2i -6i² / (4 - 4i²)

but i² = 1

= 2 - 4i - 6(-1) / (4 - 4(-1))

= 2 - 4i + 6 / 4 + 4

= (8 - 4i) / 8

= 1 - i / 2

The quotient write in standard form = 1 - i / 2.